Question

In the figure below, a steel bar sitting on two parallel metal rails, connected to each other by a resistor, is pulled to the right with a constant force of magnitude F_app = 1.40 N. The friction between the bar and rails is negligible. The resistance R = 8.00 ?, the bar is moving at a constant speed of 1.85 m/s, the distance between the rails is l, and a uniform magnetic field B is directed into the page. (a) What is the current through the resistor (in A)? 0.57 A (b) If the magnitude of the magnetic field is 3.10 T, what is the length l (in m)? 0.79 m (c) What is the rate at which energy is delivered to the resistor (in W)? 2.59 W (d) What is the mechanical power delivered by the applied constant force (in W)? 2.59 W What If? Suppose the magnetic field has an initial value of 3.10 T at time t = 0 and increases at a constant rate of 0.500 T/s. The bar starts at an initial position x0 = 0.100 m to the right of the resistor at t = 0, and again moves at a constant speed of 1.85 m/s. Derive time-varying expressions for the following quantities. (e) the current through the 8.00 ? resistor R (Use the following as necessary: t. Assume I(t) is in A and t is in s. Do not include units in your answer.) I(t) = (f) the magnitude of the applied force F_app required to keep the bar moving at a constant speed (Use the following as necessary: t. Assume F_app(t) is in N and t is in s. Do not include units in your answer.) F_app(t) =

          In the figure below, a steel bar sitting on two parallel metal rails, connected to each other by a resistor, is pulled to the right with a constant force of magnitude F_app = 1.40 N. The friction between the bar and rails is negligible. The resistance R = 8.00 ?, the bar is moving at a constant speed of 1.85 m/s, the distance between the rails is l, and a uniform magnetic field B is directed into the page.

(a) What is the current through the resistor (in A)? 0.57 A
(b) If the magnitude of the magnetic field is 3.10 T, what is the length l (in m)? 0.79 m
(c) What is the rate at which energy is delivered to the resistor (in W)? 2.59 W
(d) What is the mechanical power delivered by the applied constant force (in W)? 2.59 W

What If? Suppose the magnetic field has an initial value of 3.10 T at time t = 0 and increases at a constant rate of 0.500 T/s. The bar starts at an initial position x0 = 0.100 m to the right of the resistor at t = 0, and again moves at a constant speed of 1.85 m/s. Derive time-varying expressions for the following quantities.

(e) the current through the 8.00 ? resistor R (Use the following as necessary: t. Assume I(t) is in A and t is in s. Do not include units in your answer.)
I(t) =

(f) the magnitude of the applied force F_app required to keep the bar moving at a constant speed (Use the following as necessary: t. Assume F_app(t) is in N and t is in s. Do not include units in your answer.)
F_app(t) =

In the figure below, a steel bar sitting on two parallel metal rails, connected to each other by a resistor, is pulled to the right with a constant force of magnitude Fapp = 1.40 N. The friction between the bar and rails is negligible. The resistance R = 8.00 ?, the bar is moving at a constant speed of 1.85 m/s, the distance between the rails is l, and a uniform magnetic field B is directed into the page.

(a) What is the current through the resistor (in A)? 0.57 A
(b) If the magnitude of the magnetic field is 3.10 T, what is the length l (in m)? 0.79 m
(c) What is the rate at which energy is delivered to the resistor (in W)? 2.59 W
(d) What is the mechanical power delivered by the applied constant force (in W)? 2.59 W

What If? Suppose the magnetic field has an initial value of 3.10 T at time t = 0 and increases at a constant rate of 0.500 T/s. The bar starts at an initial position x0 = 0.100 m to the right of the resistor at t = 0, and again moves at a constant speed of 1.85 m/s. Derive time-varying expressions for the following quantities.

(e) the current through the 8.00 ? resistor R (Use the following as necessary: t. Assume I(t) is in A and t is in s. Do not include units in your answer.)
I(t) =

(f) the magnitude of the applied force Fapp required to keep the bar moving at a constant speed (Use the following as necessary: t. Assume Fapp(t) is in N and t is in s. Do not include units in your answer.)
Fapp(t) =

Added by Matthew M.

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